The field of the invention deals with a problem of mechanically sharpening a continuous bandsaw blade in a "folded" condition, i.e., looped on itself to form a plurality of loops in a coiled configuration. A continuous bandsaw blade in its unfolded or extended condition is a single continuous loop. It can be folded, however, in such a manner to create a plurality of loops resembling a coil configuration. Instead of having to sharpen a bandsaw loop in its full extended position, i.e., in a single loop configuration, it would be desirable to sharpen the same bandsaw loop while it was folded. A single bandsaw loop folded to create a plurality of loops creates a coiled package much smaller in size and far easier to handle then a single loop. Sharpening of a bandsaw blade in this small package is the problem solved by the instant invention.